Epidemiology and applied statistics review module 5 sample size power and test characteristics
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Epidemiology and Applied Statistics Review Module 5 – Sample Size & Power and Test Characteristics. American College of Veterinary Preventive Medicine Review Course Katherine Feldman, DVM, MPH, DACVPM kfeldman@umd.edu 301-314-6820. Plan. Students review modules on their own

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Epidemiology and Applied Statistics ReviewModule 5 – Sample Size & Power and Test Characteristics

American College of Veterinary Preventive Medicine Review Course

Katherine Feldman, DVM, MPH, DACVPM

kfeldman@umd.edu

301-314-6820


Plan

  • Students review modules on their own

  • Send questions by email to Katherine Feldman (kfeldman@umd.edu) by Friday March 23 a.m.

  • Conference call Friday March 23 2-3 p.m.

    • Watch email and Blackboard for conference call details


References

  • Gordis L. Epidemiology, 3rd ed. Elsevier Saunders, Philadelphia, 2004.

    • $47.95 from Amazon.com

  • Norman GR, Streiner DL. PDQ statistics, 3rd ed. BC Decker Inc., Hamilton, 2003.

    • $17.79 from Amazon.com


Sample Size & Power


Effect of Sample Size

  • If a study has an inadequate sample size, then a result with a null finding (no statistically significant association detected) is uninformative

  • A true lack of association is difficult or impossible to distinguish from a true association that cannot be detected statistically because of inadequate power


Type I error

  • α is the false-positive error rate, the probability of making a Type I error (α is the level of p-value at which you reject H0, often 0.05)

  • Even if H0 is true, in repeated samples, we will reject H0 a proportion α of the time (we detect a difference when one doesn’t exist)


Type II error

  • β is the false-negative error rate, the probability of making a Type II error

  • Traditionally, β = 0.20. Thus, there is a 20% chance of failing to reject H0 when the alternative is true


Power

  • The power of a test (1 – β) is the probability of rejecting H0 when HA is true, i.e.,detecting a difference when one really exists!

  • We want power to be as large as possible


Trade-off Between α and β

  • Both types of error should ideally be minimized

  • However, a decrease in one type of error is achieved at the expense of an increase in the other

  • For a given α and magnitude of effect (RR or OR), β can be reduced only by increasing the sample size


Sample Size Calculations

  • Should be done at start of study to ensure enough power

  • To calculate need to know:

    • Desired values for the probabilities of α and β

    • Baseline (nondiseased or nonexposed) exposure or outcome rates

      • Often based on previous studies or reports

    • Expected magnitude of effect (RR or OR)

      • Often based on previous studies or reports

      • The minimum effect the investigator considers worth detecting

    • Formula

      • Varies by study design, research question and type of data

  • No formulae presented here…


Test Characteristics


Test Accuracy

  • How good is the test at identifying individuals with and without the disease?”

  • The sensitivity of the test is the likelihood of a positive test among those with the disease

  • The specificity of the test is the likelihood of a negative test among those without the disease


Test Accuracy

How good is the test at identifying individuals with the disease?

How good is the test at identifying individuals without the disease?


Test Accuracy

  • To calculate the sensitivity and specificity, we must know the truth in the population from another source, a gold standard

    • May be another test result that has been in use, and sometimes it is the result of a more definitive and often more invasive test

  • There is an inverse association between sensitivity and specificity, and therefore one must trade one for the other


Predictive Value

  • Predictive value positive (PVP)

    • If the test results are positive for this patient, what is the probability that this patient has the disease?

  • Predictive value negative (PVN)

    • If the test result is negative, what is the probability that this patient does not have disease?


Predictive Value

Likelihood of having the disease among those with a positive test

Likelihood of not having the disease among those with a negative test


Predictive Value

  • Sensitivity and specificity are test characteristics and do not vary

  • Predictive value, however, affected by

    • Prevalence of disease

      • Low prevalence of disease results in low predictive value

      • Test results must be interpreted in the context of the disease prevalence in the population

      • Most productive and efficient to use test in “high prevalence” populations, e.g., high risk

    • Specificity of test

      • The higher the specificity the higher the predictive value


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